Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 182, pp. 116.
Reconstructing the potential function for indefinite
SturmLiouville problems using infinite product forms
Mohammad Dehghan, Ali Asghar Jodayree
Abstract:
In this article we consider the linear secondorder equation of
SturmLiouville type
where
is a real parameter,
is the potential function
and
is the weight function. We use the infinite product
representation of the derivative of the solution to the differential equation
with DirichletNeumann conditions, and for the system of dual equations
which is needed for expressing inverse problem and for retrieving potential.
It must be mentioned that the weight function has a zero whose order
is an integer called a turning point.
Submitted July 15, 2013. Published August 7, 2013.
Math Subject Classifications: 34B24, 34A55, 34E20, 34E05.
Key Words: Indefinite SturmLiouville problem; turning point; dual equations;
infinite product form.
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Mohammad Dehghan
Faculty of Mathematical Sciences
University of Tabriz
Tabriz, Iran
email: mdehghan@tabrizu.ac.ir, Tel. +989113512619


Ali Asghar Jodayree
Faculty of Mathematical Sciences
University of Tabriz
Tabriz, Iran
email: akbarfam@yahoo.com

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